The Vertical City:

Rent Gradients, Spatial Structure, and Agglomeration Economies

Crocker H. Liu
Robert A. Beck Professor of Hospitality Financial Management
School of Hotel Administration
Cornell University
Phone: (607) 255-3739
chl62@cornell.edu

Stuart S. Rosenthal
Maxwell Advisory Board Professor of Economics
Department of Economics and Center for Policy Research
Syracuse University Syracuse, New York, 13244-1020
Phone: (315) 443-3809
ssrosent@maxwell.syr.edu

William C. Strange
RioCan Real Estate Investment Trust
Professor of Real Estate and Urban Economics
Rotman School of Management
University of Toronto, Toronto Ontario M5S 3E6, Canada
Phone: (416) 978-1949
wstrange@rotman.utoronto.ca

November 3, 2016

We thank Laurent Gobillon and Anthony Yezer for helpful comments, as well as seminar participants at
the University of Pennsylvania, George Washington University, the University of Cincinnati, the Board
of Governors of the Federal Reserve System, the Cleveland Federal Reserve Bank, the 2015
UEA/NARSC Conference in Portland, and the 2016 AREUEA-ASSA Meetings in San Francisco. We
also thank Daniel Peek and Joseph Shaw for valuable discussions on commercial buildings and leases. In
addition, we thank several commercial real estate organizations for providing us with access to their
offering memoranda. CompStak data were obtained with support from the Center for Real Estate and
Finance at the School of Hotel Administration at Cornell and also from the Maxwell School at Syracuse
University. Strange acknowledges financial support from the Social Sciences and Humanities Research
Council of Canada and the Centre for Real Estate at the Rotman School of Management. Nuno Mota,
Sherry Zhang, Jindong Pang, and Boqian Jiang provided excellent research assistance. Errors, of course,
are the responsibility of the three authors.
 Abstract
Tall commercial buildings dominate city skylines. Nevertheless, despite decades of research on
commercial real estate and horizontal patterns of urban development, vertical patterns have been largely
ignored. We document that high productivity companies locate higher up, with less productive offices
lower down and retail at ground level. These patterns reflect tradeoffs between street access and vertical
amenities. Vertical rent gradients are non-monotonic, independent of nearby employment, and large.
Doubling zipcode employment increases rent by 10.5%, indicating the presence of agglomeration
economies. Moving up one floor has the same effect on rent as adding 2,500 workers to a zipcode.

JEL Codes: O18 (Economic Development: Urban, Rural, Regional), R30 (Real Estate Markets, Spatial
Production Analysis, and Firm Location: General)

Key Words: Commercial real estate, vertical, agglomeration economies.

I. Introduction
Tall commercial buildings define city skylines and are equivalent in scale to small cities. To take
one famous example, the World Trade Center’s twin towers together had roughly 50,000 workers in 10
million square feet of space, making each equivalent in size to a small town.1 The twin towers were part
of the vast commercial real estate industry. As of 2009, the aggregate value of commercial real estate in
the United States was in excess of 11 trillion dollars (Florance et al., 2010). Nevertheless, despite
decades of research on commercial real estate and on horizontal patterns of urban development, vertical
patterns within cities have been largely ignored.2 As a consequence, the extent to which different types of
companies sort into different vertical locations, analogous to extensively studied horizontal sorting, is
poorly understood. Are the most productive law offices, for example, high up off the ground, consistent
with industry folklore that suites up high are prestigious? If so, what may drive such sorting outcomes
and how does vertical sorting affect rent? The answers to these questions are not obvious because higher
commercial rents must be offset in equilibrium by higher revenue or reduced operating costs, given the
profit motive of commercial tenants.
Systematic vertical variation in rents must also be reconciled with previous estimates of spatial
variation in productivity in urban areas. The agglomeration literature has emphasized that proximity to
nearby employment often increases productivity by enhancing the ability of businesses to draw on pools
of skilled labor, share intermediate inputs and learn from their neighbors (e.g. Rosenthal and Strange,
2004; Combes and Gobillon, 2015; Behrens and Robert-Nicoud, 2015). Again though, studies of this sort
have been carried out exclusively in a horizontal context, even those taking a microgeographic approach
(e.g. Rosenthal and Strange, 2003; Arzaghi and Henderson, 2008). Moreover, while a stylized fact
emerging from numerous studies in the agglomeration literature is that doubling nearby employment
increases wage by 2 to 5 percent (e.g. Rosenthal and Strange, 2004, 2008; Combes and Gobillon, 2015),
the agglomeration literature has largely ignored rent. By how much does the scale of nearby employment
boost commercial rent and how does that relationship compare to the wage elasticities just noted? Are
estimates of the rent-agglomeration elasticity sensitive to the vertical location of establishments, and
conversely are estimates of vertical rent gradients sensitive to the scale of nearby employment? As will
become apparent, answers to these questions can illuminate the nature of the underlying drivers of vertical
and horizontal patterns of sorting and productivity, as well as whether those mechanisms are similar or
different.

1
See https://www.nysm.nysed.gov/wtc/about/facts.html.
2
The focus on horizontal patterns of spatial sorting in urban areas is evident in literature reviews by Brueckner
(1987) and Duranton and Puga (2015). In addition, as discussed in greater detail below, the few recent papers on tall
buildings (e.g, Barr, 2012, Koster et al, 2014a, Ahlfeldt and McMillen, 2015) have focused on building height rather
than internal structure.
 For at least two reasons, the need to know more about these issues will grow over time. The first
is that the number of skyscrapers worldwide is growing at a dramatic rate.3 Thus, an increasing amount
of aggregate employment is housed in tall buildings, and failing to allow for the vertical organization of
economic activity risks missing much of what may contribute to urban productivity. Second, the business
service sector continues to grow relative to the rest of the economy but most of the agglomeration
literature has focused on manufacturing that is declining in employment share and tends to operate in low-
rise buildings outside of city centers. The business services sector, in contrast, increasingly dominates
city centers and operates disproportionately in tall buildings.4 As economies continue to evolve in this
direction, the need to understand more about the vertical organization of urban areas and the office sector
will grow.
This paper addresses the questions highlighted above, and in doing so it makes a number of
contributions to the literature. We begin by adapting the standard monocentric model of urban spatial
structure of Alonso (1964), Mills (1967), and Muth (1969) to activity inside tall buildings. This yields
new insights into spatial sorting in a manner that points to a series of sharp testable predictions. These
predictions are then tested using three unique databases, two of which have only just become available.
Data sources include confidential offering memoranda that lay out the tenant stack (tenant locations) and
rents by floor for 93 tall buildings spread across 18 metropolitan areas, a new commercial rent dataset
produced by CompStak Inc., and establishment-level data on employment, sales and more from Dun and
Bradstreet (D&B). Details of these data are provided later in the paper. For now, it is sufficient to
emphasize that these data allow us to examine features of commercial buildings that have not been
feasible to study in the past.
Our theory treats each building as a “long narrow city” in the sense of Solow and Vickrey (1971).
At the core of the model is a tension between vertical transportation costs – the cost of accessing the street
– and vertical amenities, both of which increase moving up within a building. Vertical transportation
costs are large. Evidence from an IBM (2010) survey of office tenants, for example, suggests that a
typical tenant spends 22.36 minutes waiting for or riding in elevators in a business day. This is close to
the average one way home to work commute of 24 minutes as reported in the Census (Rosenthal and

3
The burst in skyscraper construction has included several successive tallest buildings in the world (Petronas
Towers, Taipei 101, and Burj Khalifa). There has also been a skyscraper boom in New York, as well as in other
North American cities. See Economist (2015) and http://www.nationalgeographic.com/new-york-city-skyline-
tallest-midtown-manhattan/ .
4
In 1950, for example, manufacturing accounted for roughly 30 percent of U.S. nonfarm employment while
professional and business services accounted for just 6.5 percent. In 2016 those shares had shifted to 8.5 percent
and 14.1 percent, respectively (U.S. Bureau of Labor Statistics, www.bls.gov). Adding health and education
services to professional and business service employment counts, the combined employment shares of these
segments of the service sector accounted for just 11.4 percent of employment in 1950 but 29.8 percent in 2016.

2
Strange, 2011).5 Vertical amenities matter to commercial tenants only to the extent that they raise
profits.6 We discuss below that this may be because views or simply the status associated with height can
impact value both by acting as perquisites for employees and by signaling productivity to potential
customers. In both cases, a high location will be worth more to a high-productivity tenant. These
modeling features imply that high productivity amenity-oriented office establishments should sort into
suites higher up off the ground with less productive offices lower down and access-oriented
establishments like retail concentrated at ground level. We show that these patterns should also support a
non-monotonic, nonlinear vertical rent pattern: ground floor rents should be high relative to the third floor
because of easy street access, but should then rise gradually and at an increasing rate with additional
height as amenities become more dramatic. It is important to recognize that the mechanisms in our model
that drive vertical sorting are quite different from the micro-foundations that are thought to generate
productivity spillovers from nearby employment. If our modeling structure is correct, a further prediction
therefore is that the vertical rent gradient should be independent of the scale of nearby employment and
the influence of nearby employment on commercial rent should be unaffected by a company’s vertical
location.
Empirical results support the model’s predictions in addition to yielding the first ever estimates of
the vertical rent gradient and a robust estimate of the elasticity of commercial rent with respect to the
scale of nearby employment. For a typical tall building (over 30 floors), moving up from the ground floor
to the second floor, rents drop by up to 50 percent. Moving up from the second floor causes rent to
increase by roughly 0.6 percent per floor with a steeper rent gradient high up off the ground (e.g. above
floor forty). Adding controls for the scale of nearby employment allows for both vertical and horizontal
drivers of rent. In those models, doubling employment in an establishment’s zipcode increases
commercial rent by roughly 10.5 percent.7 This implies that adding 2,500 workers to a building’s zipcode
increases rent by an amount about equal to moving up one floor. Consistent with wage and other
agglomeration studies, we also find that the impact of within-building employment on commercial rent is
more than three times larger than the effect of zipcode employment outside of the building. This echoes
findings in Rosenthal and Strange (2003, 2004, 2005, 2008, and 2012) and Arzaghi and Henderson (2008)
that agglomeration economies attenuate sharply with distance. As also predicted, estimates of the vertical

5
Glaeser (2011) and Bernard (2014) argue that prior to the elevator, residential buildings were typically under six
stories, with the top occupied by the lowest income tenants. Elevators dramatically reduced the cost of vertical
travel which, along with steel and other technology, was crucial for making tall buildings viable.
6
The situation is different for residential buildings where view and height enter directly into tenant utility functions.
Deng et al (2016) document that views increase condominium values in tall residential buildings in Vancouver. See
also Pollard (1980, 1982), Sirmans et al (2005), and Rodriguez and Sirmans (1994) for related evidence that scenic
views increase residential property values.
7
This is larger than the agglomeration literature’s 2-5 percent estimates of the MSA-level wage-agglomeration
elasticity.

3
rent gradient are unaffected by controls for nearby employment while estimates of the elasticity of nearby
employment on commercial rent are unaffected by controls for the vertical pattern of rents. Our findings,
therefore, confirm that both horizontal and vertical attributes have an important effect on commercial rent
and that these effects are largely independent of each other.
The paper’s final set of empirical results pertain to sorting and again support the theory’s
predictions. Using the D&B data, we proxy for establishment productivity for single-site establishments
using sales per worker and the number of workers at the site. For headquarter establishments we also
control for employment at the firm level and replace establishment-level sales per worker with its firm-
level analogue. Results from these and other models confirm that access-oriented establishments like
retail are concentrated at the ground level, while amenity-oriented establishments like law offices tend to
be higher up. Moreover, compelling evidence confirms that the most productive offices
disproportionately occupy suites in the upper portions of tall buildings while less productive offices tend
to be lower down. As with the rent models, these estimates are extremely robust and persist regardless of
controls for fixed effects at the MSA, zipcode, or building level.
The patterns above extend several distinct lines of research. As noted previously, the paper
builds directly on the literatures on urban spatial structure and on agglomeration economies. The paper
also builds on extensive previous work on commercial real estate. Studies in this area have considered
the return on investment in commercial real estate using REITS and cap rates (e.g. Kalberg et al, 2008,
Plazzi et al, 2010), the influence of vacancy rates on office rents (Wheaton and Torto, 1988, Glascock et
al, 1990), and retail malls including the role of anchor tenants.8 These sorts of studies, however, have
only lightly touched on spatial issues and have overlooked vertical issues entirely.9
Our work builds most directly on research that considers building height and the effect of
building height on building value and rent. Helsley and Strange (2008) present a game theoretic model
where builders derive payoffs from having a tall building independent of the rents that might accrue.
Ahlfeldt and McMillan (2015) document a robust positive relationship between building heights and land
rents using Chicago microdata that spans more than a century. They also show that spatial dispersion of
tall buildings can be explained in part by the dissipative competition for height modeled by Helsley and
Strange. Barr (2010, 2012) carefully documents patterns of building heights in Manhattan. Colwell et al
(1988) and Shilton and Zaccaria (1994) provide evidence that commercial building values increase with
building height for Chicago and Manhattan, respectively, while Koster et al (2014a) use data from the

8
This includes theoretical work by Brueckner (1993) and Konishi and Sandfort (2003) and empirical studies by
Gould and Pashigian (1998) and Gould, Pashigian, and Pendergast (2005).
9
There is also a tendency in the commercial real estate literature to take rents as primitive and then compute asset
values, capital structures, or asset allocations based on these primitive prices (see, for instance, the textbook by
Geltner et al, 2007). This paper differs in that we explicitly model the determinants of rent based on underlying
sorting outcomes.

4
Netherlands to show that commercial rents are higher in taller office buildings. Koster et al argue that
their rent patterns can reflect scenic views from tall buildings or the landmark nature of the structures
themselves. Dericks and Koster (2016) examine current day neighborhoods in London that were bombed
during the blitz in World War II. They argue that previously demolished areas were rebuilt to higher
density and provide evidence that commercial rents are higher in such locations. Jennen and Brounen
(2009) examine the Amsterdam office market and report evidence that doubling the number of buildings
in an office cluster increases commercial rent by 4.5 percent. The fundamental difference between our
paper and the existing literature on building height is that we observe and evaluate what happens inside of
tall buildings including vertical spatial patterns of sorting, employment, productivity, and rent.10
The remainder of the paper is organized as follows. Section II presents our theoretical model and
highlights predictions that will be examined in the data. Section III describes the unique data that make
the paper’s analysis possible. Section IV computes and compares vertical and horizontal rent gradients,
while Section V presents estimates of vertical sorting patterns among office establishments. Section VI
concludes.

II. A theory of vertical bid rent and spatial structure

This section lays out a theory of the vertical allocation of activities to commercial space. The
demand structure is stylized, with rents depending on two factors: access to the ground floor and
amenities that rise (in some situations) with height off the ground. As noted above, the concept of
amenities is quite different for the commercial space that we consider here than for residential space. We
cannot simply borrow from the more developed residential amenities literature, and so we will develop
more precisely below the way that height can contribute to profit. The section will proceed incrementally,
beginning with the vertical bid rent of the retail tenants of one building. These tenants are assumed to
care only about access. We then move on to consider office tenants who care about both access and
amenities. We then consider both sorts simultaneously. The model generates a number of predictions
that will be the basis of the empirical analysis that comprises the remainder of the paper.

A. Retail activities
Consider a building with a large pool of potential retail tenants. In this “open” framework,
potential tenants bid for locations. Each tenant consumes a fixed amount of space, s, normalized to unity.
Each tenant employs a fixed number of workers, n, also normalized to unity. These and other simplifying
assumptions are relaxed later in the section.
10
The data used by Koster et al (2014a) include a small number of observations for which it is possible to observe
the floor on which an office suite is located. However, their data are not rich enough to allow for the sort of analysis
conducted in this paper.

5
 The tenants serve a pool of customers of size M. This includes both customers from outside the
building and also those who work in the building and also make purchases there. We assume that both
groups appear at the ground floor of the building. Each tenant has the potential to serve a share of these
customers. A given customer may buy from multiple tenants, for instance shoes and a shirt. Supposing
that customers are matched with particular tenants is a convenient way to capture this sort of matching.11
A customer’s gross utility from a purchase is v. The customer incurs two sorts of cost, a price p that is set
by the retailer and the vertical transport costs associated with the trip from the ground floor to another part
of the building. Let the retailer be located on floor z.12 Then transport costs associated with buying from
the retailer equal Rz. The customer will buy from every retailer with which there is a match provided the
total costs incurred, both price and access costs, are sufficiently low relative to the utility generated from
a purchase.
The retailer incurs three sorts of costs, labor, rent, and other costs. For retailers, we will simply
suppose labor costs equal a fixed retail wage wR for its one unit of labor. A retailer incurs marginal cost
of c for each customer it serves. The total rent paid by a retailer on floor z is sr(z), which equals r(z) with
the normalization s = 1.
A retailer located on floor z chooses price to maximize its profits. In this setup, retailer profit
equals

(z) = (p-c)m(z,p) – wR – r(z), (II.1)

where m(z,p) gives the number of consumers served on floor z at a price of p. If p ≤ v - Rz, then the
tenant serves its share of potential customers, m(z,p) = M. In this region, the profit-maximizing price
would be p = v - Rz. If p > v - Rz, the firm serves zero customers, m(z,p) = 0, because the customers are
deterred from buying the good by its price. Taking rent and labor costs as fixed for now, the retailer will
choose to serve its customers when p = v - Rz ≥ c.
In this setup, the retailer reduces price at higher floors to keep from losing customers. It extracts
the entire surplus from the transaction. The retailer then serves its full share of customers, M, as long as
it is capable of earning non-negative profit by doing so. Profit may be re-written as,

(z) = (v - Rz-c)M – wR – r(z). (II.2)

11
It is worth pointing out that spatial competition among tenants in the spirit of Hotelling is a much less tractable
model. Since this section’s model is meant to illustrate the roles of access and amenities, we have opted for
tractability.
12
With a multi-floor retailer, access costs would depend on the floor on which a particular department is found. We
ignore the details of this by treating each retailer as being located on one floor.

6
As usual, in an open model of this sort, bidding among potential tenants results in rent adjusting to give
zero profit. The retailer bid-rent is thus

r(z) = M(v - Rz-c)– wR. (II.3)

There are two features of retail bid rent that are important for our purposes. First, retailer bid-rent
is negatively sloped,

∂r/∂z = -MR < 0 (II.4)

Rent falls as one moves to upper floors because the product becomes less accessible and thus less
attractive to consumers, resulting in a reduction in price. Other specifications of demand would lead to a
similar conclusion. For instance, if consumers differed in the utility that they received from purchase,
then the firm would trade-off price and quantity as usual. Higher locations would offer a less favorable
tradeoff, leading to the reduction in rent. The negative slope discussed here depends crucially on the
assumption that amenities are typically not important for retailers. We believe this to be correct most of
the time. One notable exception is high floor restaurants, where the view is bundled with the meal, and
customers may be willing to pay more at higher floors. The analysis in the next subsection can be
employed to capture this.
The second key feature of retail bid rent is that at a sufficiently high location, retail-bid rent
becomes negative. Setting r(z) from (II.3) equal to zero, gives

z* = [M(v -c)– wR]/MR. (II.5)

When access is sufficiently poor, retailers cannot make competitive bids for space. Retailers will not,
therefore, occupy this space.
We now turn to the office tenants who can make positive bids for these higher floors.

B. Office activities
Suppose the demand structure for office activities is parallel to the structure for retail activities.
Specifically, there is a pool of customers at street level of size N. Customers incur access costs, denoted

7
O. As above, an office tenant will serve a share  of these customers as long as its price is less than or
equal to the gross utility from the purchase, pO ≤ v - Oz.13
There are two important differences between the demands for office and retail. First, the costs of
accessing the higher floors are lower for office transactions than for retail transactions. Let O denote
vertical transport costs in the office sector, with O R. The assumption that vertical transport costs in
retail are high reflects that these trips are typically taken with a slow mode of travel such as stairs or an
escalator. Office trips are typically taken with a fast mode, such as elevators. Finally, it may take fewer
trips by the customer to create value. For instance, Ascher (2011) suggests that this is true for law offices.
Any of these will result in the ranking we have assumed for vertical transportation costs. This ranking
will generate a sharp empirical prediction, one that will be tested later in the paper.14
The second difference between office and retail tenants is that some valuable “amenity” may
accrue to the tenant from its high location. In the case of a residential high-rise, the amenity is easy to
understand. Views are better and noise is minimized at high levels. In addition, there may be prestige
associated with high locations. These effects result in a high-floor premium in residential buildings.
The role of amenities, broadly conceived, is more complicated in commercial real estate. One
possibility is that the consumers of the firm’s output value the output more if it is purchased on a high
floor. It is difficult to believe that this can account for a large enough increase in revenues to generate the
patterns discussed in the Introduction and that will be explicated in detail below. A more plausible
explanation is that there is signaling. Signaling has been offered as an explanation for various corporate
activities, including the issuance of dividends, the provision of CEO mansions, and the purchase of lavish
office space.15 The heart of the signaling argument here would be that occupying a high floor indicates
unobservable elements of the value of service to customers, resulting in greater revenue at high floors.
Yet another amenity effect operates through the labor market. While customers are likely to
spend little time enjoying the view from a high floor office that they visit, employees spend considerable
time in their offices. An office with a commanding view is an important and visible perquisite, one that is
likely to be valued by employees. This is especially so since many classes of office workers have high

13
It is straightforward to consider differences in utility, v, between retail and office customers. This will not affect
the slope of bid rent, but it will affect the level.
14
We have ignored the fixed costs of taking an elevator and the related decision of whether to walk between floors
or take an elevator. In our model, the assumption that vertical transport costs for retail are higher than for office
should be interpreted as capturing the willingness of customers to walk a few floors even at high cost in the presence
of fixed costs for the low per-floor technology of the elevator.
15
Miller and Rock, (1985) is a seminal reference on dividends as signals.

8
incomes, which is likely to raise the value they would assign to a “perk” such as a view. In this situation,
workers will accept lower wages, raising profit. This, in turn, will raise bid-rents for high floor offices.16
We capture these various amenity effects as follows. First, we suppose that revenue rises with
floor height (the first two effects). For simplicity, we suppose that the profit function is linearly
separable, with the additional revenue equal to z. Second, we suppose that worker utility rises by z,
resulting in an equal reduction in labor costs.
In this specification, an office firm’s profit equals

(z) = N(v - Oz-c) + z – (wO- z) – r(z), (II.6)

where wO is the wage required for an office worker on the first floor, consequently enjoying no amenities.
Competition among office tenants gives the office bid rent as:

r(z) = N(v - Oz-c) + z – (wO - z) (II.7)

In contrast to the bid-rent for retailers, the office bid rent is of indeterminate slope:

∂r/∂z = -NO +  +  (II.8)

Absent a strong enough amenity effect of some sort, bid-rent will fall as floor height rises, as with
retailers. The presence of a positively sloped bid-rent – as discussed in the Introduction – suggests the
presence of some sort of amenity.

C. Vertical spatial structure

In this section there are two types of tenant. Retailers are access oriented, while office employers
can be amenity oriented, supposing that the amenity effects on profit are strong enough to outweigh the
negative effects on access of moving higher up in a building. In any case, the lower level of vertical
transportation costs will tend to give office tenants a comparatively stronger orientation to amenities and a
comparatively weaker orientation to access.
The equilibrium vertical allocation of space within a building to competing potential tenants will
be determined, as in the horizontal models in the Alonso-Mills-Muth tradition, by bid rents. In the
empirical analysis to follow, we will allow for a range of differences in access and amenity orientation.

16
See for example, Rajan and Wulf (2006) for a discussion of how perks can be an important element of the utility
derived from compensation and thus be used to motivate far more cost-effectively than equivalent amounts of cash.

9
Our purpose here is to illustrate the forces at work, and we can do that in a model that has two sorts of
potential tenants, one access oriented retailer and one amenity oriented office tenant. The office tenant’s
amenity orientation is such that the bid rent is positively sloped (see equation (II.8)).
The relative positions of the two tenant types depend on the slopes of the bid rent curve.
Retailers have a negative slope, while office firms have a positive slope. It is therefore unambiguous that
office firms will occupy higher floors and retailers will occupy lower floors, provided that both types are
present. A necessary condition for the retailers to be present is that the retailers have a positive bid rent
for the bottom floor (z = 0) and can outbid the offices there. A necessary condition for the office firms to
be present is that they have a positive bid rent for the top floor (z = Z) and can outbid the retailers at the
top of the building. These require, respectively, that

M(v -c)– wR > N(v - c) – wO (II.9)

and

N(v - OZ-c) + Z– (wO - z) > M(v - RZ-c)– wR. (II.10)

(II.9) will hold if retail demand, M, is large enough relative to office demand, N. (II.10) will hold if
the difference in access costs is large, R-O, and amenities are valuable either to customers or as a signal,
, or to workers, . These conditions will give a building divided into retailers below and office tenants
above.
In reality, there is obviously a much finer gradation of tenants according to their access and
amenities orientation. Tenants with greater access orientation will tend to be lower in the building, while
those with greater amenities orientation will tend to be higher. This is an important extension of the
classic analysis of urban spatial structure. To the extent that firms do indeed differ in their access and
amenities orientations, then we will not see a single land use at a particular street address in a business
district. Instead, establishment types will sort both horizontally and vertically, with certain types of
activities found at different heights above ground level.
The following are the key implications of this section’s theory:

(i) The vertical rent gradient will be non-monotonic, falling with height at the lowest floors,
and later rising at the highest.

(ii) Retail tenants will occupy the lowest floors, while office tenants will occupy the highest.

10
In addition, as noted above, firms will tend to have a stronger amenity-orientation when the view is
somehow more valuable to either their workers or their customers, possibly as a signal. In a signaling
equilibrium, high type firms signal their type by locating high. In the case of workers and amenities, and
assuming that dramatic views are normal goods, high productivity establishments that rely on highly paid
workers will outbid others for office suites up high. Accordingly, a third prediction of our theory is:

(iii) Among amenity-oriented establishments, higher productivity companies will sort into
higher floors with lower productivity companies lower down.

Taken as a group, the predictions above all mean that verticality matters, both in pricing and spatial
structure.

D. Extensions
The model has been specified parsimoniously to allow us to illustrate how the tension between
amenity and access orientation governs vertical sorting in buildings and the accompanying equilibrium
rent relationship. This section will sketch some extensions that bear on the empirical analysis to follow.
The first concerns the horizontal structure of cities. This is the subject of traditional monocentric
analysis. Our model extends easily to incorporate horizontal factors that affect commercial rent. Suppose
that x gives the distance to the predetermined center of the city. At greater distances, employment
declines along with the number of companies seeking space for retail and office activities. The decline in
employment density also lowers productivity by reducing spillovers from nearby employment. Together
these forces lower demand for space in commercial buildings and can be captured by making the demand
variables functions of x. If M(x) and N(x) decline in x, then we have the result that bid rents for both
retail and office tenants decline with horizontal distance. Equivalently, if N and M capture nearby
employment density, these arguments imply that bid-rents for retail and office tenants decline with
density.
The second concerns the “captive” retail demand that comes from other tenants in the building. If
M depends on building height, then it is immediate that retail rents will be larger at the bottom of tall
buildings and that retail will be a more competitive bidder for space, ultimately occupying more floors in
equilibrium. This also implies that the ground floor rent premium relative to rents just above ground level
will be larger in taller buildings. Since buildings will tend to be taller near the city center when rents are
higher, captive demand and horizontal structure will tend to work in the same direction.

11
 The third concerns the management of the building. This is more complicated, suggesting the
possibility of the allocation of space depending on non-Walrasian forces that are absent from standard bid
rent analysis. See Han and Strange (2015) for a survey of search models for housing, and see Grenadier
(1995) for a rare instance of a non-Walrasian model of space for the commercial sector. The issue is that
a landlord may not simply allocate space to the highest bidder if the discounted expected value of another
bidder’s payments would be greater over the duration of the contract. For instance, a tenant who offers
high rent but also has a high likelihood of default will not be preferred to one who offers almost as much
rent but has a very low default probability. This sort of calculation is likely to be most important at the
top of a building, where rents are highest.
These extensions suggest an additional three predictions that can be empirically tested:

(iv) Rents will be higher in dense central locations.

(v) Ground floor rent premium will depend on building height.

(vi) Tenant risk will impact the allocation of space.

It is worth emphasizing that all of the model’s predictions (i to vi) are driven by the tradeoff
between the cost of street access and amenities, both of which are assumed to increase with height. This
is completely different from the agglomeration spillover literature in which horizontal variation in rent
(and wage) is thought to be driven by distance to employment centers and related spatial variation in
productivity arising from opportunities to share labor, physical inputs and knowledge. Our modeling
structure, therefore, points to two further predictions that will also be tested:

(vii) The vertical rent gradient should be independent of the scale of nearby employment.

(viii) The elasticity of commercial rent with respect to nearby employment should be
independent of the vertical location of a tenant.

III. Data
A. Three primary data sources
The data for this paper are unique and open up a new set of opportunities for research on the
spatial structure of cities. We draw upon three primary data sources, each of which is described in detail

12
below. Collectively, our data enable us to observe actual commercial rents paid, the identity and location
of establishments within a given building (known as the tenant stack), and attributes of the leases.
Our first data source is a set of the confidential offering memoranda (OM) that are made available
to prospective investors when a building is up for sale. Drawing on contacts in the real estate industry,
we obtained access to such memoranda for 93 tall buildings spread across 18 metropolitan areas in the
United States that were up for sale at various times from 2003 to 2014. The memoranda typically provide
complete detail on the tenant stack in the building – the identity and location of all tenants – along with
extensive information on the cash flows, rents, and lease arrangements associated with each tenant.
While the tenant stack is public information the rent data are confidential and we are not at liberty to
share those data.
Our second key data source is from CompStak Inc., a newly created company (as of 2012) that
collects and markets data on commercial rents, leases, and other related measures for commercial
buildings for a number of major metropolitan areas in the United States. CompStak (CS) operates in
some respects as a co-operative. Commercial leasing agents are allowed to draw a specified number of
“comps” – the lease and rent terms associated with a comparable office space – for every comp that the
agent contributes to the data base. In New York city, as an example, the CS database currently includes
information on rent terms, lease, and other related attributes for roughly 24,000 office suites spread
around the city. Most of the CS data reflect agent reports submitted since 2012 for tenants that moved
into their suites between roughly 1999 to present. The nature of the CS database is that it will grow and
become more complete over time as the networking aspects of the data encourage additional agents to
participate and also with additional turnover of office suites. We currently draw on CompStak data for
buildings in New York, Chicago, Los Angeles, San Diego, Atlanta, Washington DC, San Francisco, and
the San Francisco Bay Area outside of San Francisco itself. We have selected these metropolitan areas
because they offer richer data. The list of cities for which lease comparables are collected from continues
to expand. Given our focus on tall buildings in urban areas, when drawing on the CS data, we work with
only buildings that are at least 10 stories tall (CS data also includes suites in many buildings under 10
stories tall).
The CS and OM data have different strengths and weaknesses. Both provide detailed information
on commercial office rents, leases, and the location of tenants in a building. The OM data contain
information on the complete set of tenants in a building at a given point in time. The CS data provide
information on a subset of tenants in a given building, but thousands of buildings are represented in the
database. In addition, because of the nature of the CS data collection process tenants in the CS data are
skewed towards recent arrivals, although not exclusively so. Regarding rents, the OM data report actual
rent paid at the time the offering memo was produced, while the CS sample includes effective rent, where

13
actual rents are adjusted to account for various landlord concessions such as free months of rents and
fitting out allowances. The OM data are laborious to collect as it was necessary in many instances to
transcribe information embedded in the offering memo text into a machine readable form. As an
example, Appendix A displays abbreviated information regarding the tenant mix (stacking plan) from the
offering memorandum for Prudential One and Two in Chicago with the rent information removed. These
memos were entered into the public domain as part of a CMBS (commercial mortgage backed security)
filing with the SEC (Securities and Exchange Commission).17 Appendix B displays an example of
information on rents known as the rent roll for a portion of the building known as 999 Peachtree Street in
Atlanta, Georgia which is also in the public domain through SEC filings.18 The information on rents is
similar to what is contained in our offering memorandums, but with less detail. The 93 offering memo
data used here were transcribed over a one and one-half year period from 2013 to 2015. In contrast, the
CompStak data are commercially available and are not subject to restrictions based on confidentiality.
The CompStak data also cover over 100,000 office suites spread across thousands of buildings. Not all of
the CompStak records indicate floor or suite number, however, and others contain other types of missing
information. 19 Our cleaned CompStak file with all of the key variables present includes 37,007 suites
spread across 1,922 buildings.
Our third major data source is Dun and Bradstreet (D&B), obtained through the Syracuse
University library. Rosenthal and Strange (2001, 2003, 2005, 2008, and 2012) have previously used
D&B data in a series of papers in which the data were obtained already aggregated to the 5-digit zipcode
level. Recently, Syracuse University obtained a site license with Dun and Bradstreet that permits us
(given Rosenthal’s Syracuse affiliation) to download establishment level data. Approximately, D&B data
cover the universe of establishments in metropolitan areas across the U.S. These data provide detailed
information on employment and sales at an establishment’s site (i.e. suite), establishment type (i.e. single
site, branch, headquarters), corporate status (corporation, partnership, sole proprietorship), risk attributes,
sales and employment of the overall firm for multi-site companies, and many other attributes of the
establishments. Among these other features includes the establishment’s full SIC code which we draw
upon at the 2-digit level in most applications.

17
http://www.secinfo.com/dsvrn.v4Mq.htm
18
http://www.sec.gov/Archives/edgar/data/1031316/000117152013000210/ex10-1.htm
19
As such, we also use data from CoStar, a company that collects and markets data on commercial real estate lease
and sale transactions. Currently, CoStar does not permit downloading of leases. The lease information that CoStar
reports is relatively sparse compared to CompStak. CoStar’s lease information in most cases only includes the
floor(s), suite number(s), start date of the lease, end date of the lease and in a few instances the asking rent for each
tenant. No information exists on rent concessions nor effective rent in general. The CoStar data is matched with
portions of the CS data from Chicago to fill in missing suite and floor numbers in some instances.

14
 Critical to our work, the D&B data also provides the complete street address of the establishment
which, in many instances, also indicates the floor number and/or suite number in which the establishment
is located. A limitation of the D&B data is that at most one floor number is indicated. For tenants that
occupy space on multiple floors this injects a degree of measurement error. However, we have confirmed
using the offering memo data and also CompStak that the large majority of tenants in commercial office
buildings occupy space either on a single floor or on adjacent floors. This reduces concerns about
measurement error when using floor number information from the D&B data. In addition, as will become
apparent, we use the D&B floor number data primarily when evaluating vertical patterns of productivity
for law offices and other related service areas (e.g. financial services). These sorts of companies are
especially likely to occupy space on a single floor. Moreover, floor number in these instances is used as a
dependent variable and for that reason classical measurement error does not bias our estimates.
In some applications we merge the D&B data at the tenant level with tenants in the 93 tall
buildings from our offering memos. This enables us to examine location within the tenant stacks by
industry SIC classification. In other applications we use D&B data to measure employment in a
building’s zipcode and also within the building itself, and then match that information to the CS data.20
The offering memos identify tenants only based on their name while D&B identifies tenants by
name and also their unique D&B assigned DUNS number. To match OM and D&B tenant data, we
searched the web by tenant name for each of the roughly 6,000 tenants in the offering memo data and
determined their DUNS number which was then coded to the CS file and used to match with D&B
records. The match rate was close to 70 percent from among all of the tenants in the OM data, held down
in part because the D&B data to which we have access are current whereas some of the OM data reports
tenants as far back as 2003.21 When matching zipcode-level D&B data to the CS data, the match rate was
nearly perfect as zipcode is provided in the address fields for both datasets. When matching building-
specific employment from D&B to CS data, we were forced to use street names in a given zipcode. In
this instance the match rate was roughly 85 percent.
In other portions of the empirical work to follow we rely solely on the D&B data for five select
industries in twelve metropolitan areas. Details on this portion of the D&B sample are provided later in
the paper.

20
Census data on year-2013 employment at the zipcode level based on zcta area designations was also merged with
the CS data for selected applications.
21
It is also worth noting that whereas CS and D&B emphasize accurate data on current tenants, some of our offering
memos go as far back as 2003.

15
B. Summary statistics
Table 1 provides summary measures on key data from each of the three data sources described
above. In all cases here and throughout the remainder of the paper, all dollar valued variables (e.g. rents,
sales) are reported in 2014 dollars.
Panel A summarizes the size and time period of each of the databases including number of
tenants, number of buildings, number of cities or MSAs in which buildings are located, and time period
covered. Note that in the OM data 5,750 tenant-suite observations are spread across 93 buildings in 18
cities. In the CompStak data, 37,007 tenant-suite observations are spread among 1,922 buildings in the 8
metro areas covered by CS as mentioned earlier. These include a number of well-known buildings, such
as the Empire State Building, Trump Tower, Chrysler Building, Citigroup Center, John Hancock Center
and Willis Tower. The D&B data is matched to each of the buildings in the OM and CS data as described
above. In addition, for five select industries including law offices (SIC 81), advertising offices (SIC
7311), brokerage offices (SIC 62), insurance carriers (SIC 63), and agents, brokers and services (SIC 64),
D&B data were collected for all such establishments in 12 MSAs (New York, Chicago, San Francisco,
Los Angeles, Atlanta, Washington DC, Cleveland, Detroit, Dallas, Denver, Houston, and Seattle). For
this data file we have 57,748 tenant-suite observations spread across 19,721 buildings based on the street
addresses reported in the data.
Panel B summarizes the composition of tenants in the 93 OM buildings. Summary measures are
presented for all floors combined, ground floor and below (the concourse levels), between floors 2 and
40, and floor 40 and above. We highlight the industries that are most heavily represented in commercial
office buildings. This includes retail (SIC 52-59), FIRE (SIC 60-67), business services (SIC 73), law
offices (SIC 81), and Engineering-Accounting-Management (SIC 87).
As seen in the first column, FIRE and Law offices account for 23.4 percent and 20.3 percent,
respectively of all establishments while Engineering-Accounting-Management makes up 12.1 percent.
Retail is just 6.8 percent of establishments in tall commercial buildings. A quick skim of the remaining
columns, however, indicates that the composition of activity differs sharply with height off of the ground.
On the ground floor, retail accounts for near 33 percent of establishments while law offices just 8.2
percent. From floors 3 up to 40, retail is just 2.3 percent of establishments while FIRE is 25.7 percent and
law offices are 20.6 percent. Above floor 40, retail is 3.4 percent – all of which are restaurants – and
FIRE is 25.4 percent. Law offices dominate, however, and make up 43 percent of establishments above
floor 40. These patterns provide graphic evidence of spatial stratification of activity within tall office
buildings as implied by the conceptual model discussed earlier. We will return to this point later.
Panel C provides summary measures on rent per square foot in the 93 offering memo buildings
and the 1,922 buildings drawn from the CompStak data. The average rent per square foot across the OM

16
data is $38 per square foot while for the CS data average rent is $36 per square foot. These values are
broadly consistent with the residential rents for Manhattan: a recent report indicates that the average rent
per square foot for residential space in Manhattan as of January, 2013 (in $2013) was $50.71.22
Two other important patterns are also evident in Panel C. The first is that there is considerable
variation in rents across office suites. In the OM data, rents at the 25th, 50th, and 75th percentiles are $22,
$33, and $51 per square foot. For the CS data corresponding values are $17, $33, and $49 per square
foot, respectively. The second pattern to note is that the rent distributions in the OM and CS data are of
similar general magnitude, with the effective rents from the CS data slightly lower than the actual rents
from the OM data. This provides an implicit check on the coverage and quality of the two data sources,
although differences in rents across individual buildings are to be expected.
Panel D of Table 1 characterizes the distribution of building heights across the OM and CS
samples. It does this in two ways. The first two rows of Panel D report summary statistics on building
height calculated across the buildings in the sample. Here, we see that the mean height is 32.7 stories in
the OM data and 21.5 in the CS sample. The last two rows of Panel D report summary statistics
calculated by tenant suite. There are more suites in a given tall building than in a given smaller building,
and this means that the suites in the two samples tend to be drawn more heavily from taller buildings.
The means in these samples are consequently larger, at 39.5 floors for the OM sample and 30.5 floors for
the CS sample. In the OM data, 59.9% of observations are at or above floor 30, and 10.5% are at or
above floor 60. In the CS data, 46.9% of observations are at or above floor 30, while 3.9% are at or
above floor 60. Overall, the OM sample is somewhat more skewed towards taller buildings.
Finally, Panel E reports employment for zipcodes in which CS buildings are located. Again, we
compute summary statistics in two ways, this time by zipcode and by tenant suite. Average zipcode
employment calculated by zipcode is 36,210. Calculated by tenant suite, the average rises to 85,110.
This again reflects the tendency to oversample suites from taller buildings since such buildings tend to be
located in locations with substantial employment. There is also considerable variation in employment
across our sample, with an interquartile range in the zipcode calculations of 26,170 and a larger
interquartile range when calculated by suites.
We are now able to begin reporting our results on vertical rents and spatial structure.

IV. Vertical rents

A. Baseline estimates of the vertical rent gradient and ground floor premium
Table 2a reports estimates of vertical rent gradients using the OM data (in columns (1) and (2))
and the CS data (in columns(3) and (4)). These regressions control for building fixed effects, so

22
See http://www.millersamuel.com/files/2013/02/Rental_0113.pdf .

17
identification is based on within building variation in rents. For both data sources, two models are
reported. The first regresses the log of rent per square foot on log of floor number.23 The second is a log-
linear model in which floor number is entered linearly. Additional controls are included to allow for a
ground floor premium and, in the offering memo data, a concourse (below ground floor) discount. We
allow the ground floor premium to vary with building height by including an interaction term. In all
cases, rent is reported in 2014 dollars and standard errors are clustered at the building level.
In all specifications and for both datasets, there is a large, highly significant, and positive ground
floor premium. Columns (1) and (3) report results from the double-log models. In the OM data the
premium for a 30 story building is 72 percent (equal to 30*0.007 + 0.5148) while in the CS data the
corresponding premium is roughly 33 percent. The below-ground coefficient for the OM data in column
(1) is small and not significant (the t-ratio is -0.25). Estimates for the log-linear models in columns (2)
and (4) are mostly similar. The ground floor premium for a 30 story building here is 61 percent for the
OM sample and 25 percent for the CS sample. On the other hand, the below ground discount is now large
and significant for the OM sample. These results suggest that the ground floor is especially valuable
relative to locations both just above and below ground level. The theoretical model suggests that these
findings reflect the value of access. Two additional remarks are in order. First, the advantages of the
ground floor may arise from other mechanisms than the one presented in Section II’s theory. In
particular, the ground floor provides greater exposure to foot traffic, which is likely to increase sales and
so profit. Second, the large ground floor premium is a consequence of very high transportation costs of
moving up or down one floor. This, in turn, results from the fixed costs of taking elevators, which lead
customers to walk or take an escalator (both slow) for a one floor trip instead of taking an elevator (fast).
There is also robust evidence of rents that rise with floor number beyond the second. In the
double log models (in columns (1) and (3)), the elasticities of rent with respect to floor number are 28.5
percent in the OM data and 8.6 percent in the CS data. In the log-linear models (columns (2) and (4)), a
one floor increase in height above the ground level increases rent by 1.73 percent in the OM data (with a
t-ratio of 2.73) and 0.6 percent in the CS data (with a t-ratio of 17.81). These estimates indicate that
despite rising access costs, rents rise with height off the ground. Coupled with the previously noted
ground floor premium, the vertical rent gradient is non-monotonic.
Table 2b explores these patterns further and demonstrates that the vertical rent gradient is steeper
higher up off the ground. In Table 2b, Panel A presents results for the double log model, while Panel B
presents results for the log-linear model. For each specification, the first three columns are based on OM
data while the second three columns are based on CS data. The samples are further stratified into three

23
More precisely, the key independent variable is the log of floor number + k where k is set to one unit larger in
absolute value than the lowest numbered concourse floor in the data, -5 for the OM data and -1 for the CS data.

18
groupings of floors with separate regressions for each: estimates for floors 3 to 29 are in columns (1) and
(4), estimates for floors 30 to 59 are in columns (2) and (5), and estimates for floors 60 and higher are in
columns (3) and (6).
The key result in Table 2b is that rents rise beyond the first floor at an increasing rate. Reading
across columns from lowest to highest floor groupings, in the double log specification, the rent elasticity
coefficients from the OM data are 0.1447, 0.1352, and 5.40, respectively (with t-statistics of 4.31, 0.81,
and 649.37).24 For the CS data, the corresponding coefficients are 0.0763, 0.2873, and 1.274 (with t-
statistics of 16.60, 7.29 and 4.20). Estimates for the log-linear model display a similar pattern. In the OM
sample, the gradients for the three bins are 0.82 percent, 0.33 percent, and 6.2 percent. In the CS sample,
the gradients are respectively 0.58 percent, 0.68 percent, and 1.61 percent. These estimates indicate that
the rent gradient is rather gentle for the low floors of buildings, but it becomes steeper higher up off the
ground.
The estimates in Tables 2a and 2b are completely new to the literature and have three immediate
implications. First, in contrast to the maintained assumption of the standard urban model, it is apparent
that there is not a single rent value at a given street address. Instead, within a typical building large,
systematic differences in rent are present as one moves up off the ground. Second, the fact that rents
increase with height once above the ground floor confirms that height-based amenities must be present
and that height-based amenities must increase at a rate sufficient to offset rising access costs. Third, the
tendency for rent gradients to be steeper on the higher floors of a tall building could reflect that height-
based amenities increase at a non-linear rate as one moves up above the obscuring effect of adjacent
buildings. However, a different mechanism also likely contributes to this pattern. A familiar result from
the standard monocentric model is that sorting across locations between heterogeneous agents with
different bid functions can impact the curvature of the equilibrium rent function, a principle that applies
here. The convex pattern of vertical rent gradients in Table 2b, therefore, could indicate that tenants who
place greater value on height sort into higher locations. We revisit this possibility later in the paper when
we consider more direct evidence of vertical sorting patterns. Before doing this, however, it is useful to
evaluate whether and in what fashion nearby agglomeration of economic activity affects commercial rents
and the vertical rent gradient.

B. Vertical vs. horizontal rent patterns allowing for spillovers from agglomeration
As noted earlier, standard models of urban spatial structure and productivity spillovers have
solved for spatial equilibrium patterns in a horizontal setting. Locations farther from the central business

24
It is important to note that the OM sample contains only 4 buildings above 60 stories. The high suites in these
landmark buildings (all in NY or Chicago) are clearly different from other buildings in our data.

19
district (CBD) in ground level distance will differ in employment, productivity, wages, and rents from
locations that are closer. Even though this literature recognizes that higher rents in locations offering
superior access to the CBD will prompt developers to use land more intensively, causing building heights
to rise, the buildings themselves are treated as if they were flat, with all employment at the ground level.
This section expands our rent regressions by adding controls for employment within a building’s zipcode
and also within the building itself. This will allow us to document the elasticity of commercial rent with
respect to nearby employment, a measure that is largely unknown despite being fundamental to urban
theory. The models to follow will also allow us to compare the relative magnitudes of vertical and
horizontal rent effects while shedding light on the nature of vertical versus horizontal drivers of
commercial rent.
We begin with Table 3a which presents a series of rent regressions that extend the specifications
in Table 2a. All of the models in this table are estimated using just the CS data because this data source
offers greater geographic coverage compared to the 93 buildings in the OM data. Except where noted,
building fixed effects are also replaced with MSA fixed effects as this allows us to explore the impact of
nearby employment. Columns (1) to (4) present estimates from double-log models while columns (5) to
(8) report estimates from log-linear models. For each group, the first column (columns 1 and 5) controls
only for zipcode-level employment for the zipcode in which the building is located; the second column
(columns 2 and 6) controls for vertical location and building height but omits any control for nearby
employment; the third column (columns 3 and 7) combines controls for both zipcode-level employment
and vertical location. The models in columns (4) and (8) repeat the building fixed effect models from
Table 2a. In the present context, it is worth noting that the building fixed effects capture proximity to
nearby employment as well as proximity to other valued location specific attributes. The fixed effects, of
course, also control for unobserved attributes of the buildings themselves.
In columns (1) and (5), zipcode employment has a positive and highly significant effect on rent.
In the elasticity model (column (1)), doubling zipcode employment increases rent by roughly 10.7 percent
while the gradient in the log-linear model (column (5)) indicates that adding 1,000 workers to a zipcode
increases rent by 0.23 percent (the corresponding t-ratios are 5.4 and 7.6, respectively).
These estimates confirm a core stylized fact: densely developed locations have higher commercial
rents, resulting in sharp horizontal spatial variation in office rents across business districts and cities. The
estimates are also consistent with the large literature on agglomeration economies that has established that
spatial concentration contributes to productivity. Most often, this literature has focused on wage effects
from agglomeration. As in Roback (1982), however, the productivity effects from agglomeration should
also be reflected in higher commercial rents. However, despite the strong theoretical foundations, few
papers in the agglomeration literature have used commercial rent as the outcome measure, and no

20
previous paper has looked at agglomeration economies arising from highly localized (e.g. zipcode level)
concentrations of employment using commercial rents.25 Our estimates of the rent-employment
relationship are, therefore, without precedent. Bearing this in mind, as a very rough comparison, the 10.7
percent rent elasticity obtained here is larger than corresponding wage elasticities in the literature, which
typically suggest that doubling city size increases wage by 2 to 5 percent (e.g. Rosenthal and Strange,
2004 and 2008), or by even less (Combes et al, 2008).
Columns (2) and (6) revisit the vertical rent regressions from Table 2a with the primary change
that building fixed effects are replaced with MSA fixed effects and building height has been added to the
specifications. The important point to note here is that the estimates are nearly identical, both
qualitatively and in magnitude, to those in columns (4) and (8) which repeat the Table 2a specifications.
The models in columns (3) and (7) combine the controls for zipcode employment and vertical
location as described above. Comparing estimates in these models to the employment-only and vertical-
only models yields a striking result. It is apparent that adding controls for vertical location has little effect
on the estimated influence of zipcode employment, and controlling for nearby employment has essentially
no effect on the vertical rent pattern. Moreover, the vertical rent coefficients are also nearly the same
when building fixed effects are included in columns (4) and (8). The building fixed effects, of course,
control for zipcode employment and building height, as well as a host of unobserved local and building-
specific attributes.
The remarkable stability of estimates across the models in Table 3a suggests that the processes
that drive vertical rent patterns are different from the processes that account for the positive impact of
nearby employment and other horizontal drivers of rent. The theory in Section II emphasizes the role of
vertical access costs and height-based amenities as the drivers of systematic patterns of vertical rents.
The agglomeration literature highlighted above emphasizes the positive productivity spillovers arising
from labor market pooling, sharing of intermediate inputs, and knowledge sharing (e.g. Rosenthal and
Strange (2004)). Our estimates from Table 3a are consistent with the view that these are different and
distinct underlying mechanisms that both affect commercial rents.

25
The closest paper in this regard that we are aware of is the work by Jennen and Brounen (2009). As noted earlier,
using data for commercial buildings in Amsterdam, they find that doubling the square footage of office space in a
local office cluster increases commercial rent by 4.5 percent. Drennan and Kelly (2011) and Koster et al (2014b)
also provide evidence that local agglomeration economies are capitalized into higher rent. Kelly’s analysis,
however, is an MSA-level study and in that sense focuses on much larger geographic units than used in this paper.
Koster et al (2014b) measures agglomeration at the municipality level which is smaller than an MSA but still much
larger than our geographic units. Koster et al use 1870 population density to instrument for current values of
employment density as a strategy to help address possible concerns that municipal level employment density could
be endogenous. All of these papers provide valuable evidence that commercial rents are higher in densely
developed areas. They do not, however, offer the sort of detailed within building analysis as in this paper or the
ability to measure geographic attenuation effects from nearby employment as we do in Table 3b to follow.

21
 It is also useful to consider the magnitudes of the estimates in Table 3a. For these purposes, we
focus on estimates in the log-linear model in column (7) which permits direct and intuitive comparisons
of vertical and horizontal rent patterns. For a 30-story building, the ground floor premium is roughly 28.4
percent (0.0076 * 30 + 0.056). This is roughly equivalent to the estimated increase in rent associated with
moving up 39 floors (0.0073 * 39). It is also roughly equivalent to an increase in zipcode employment of
roughly 140,000 workers, about equal to the 75th percentile among office suites in our sample (see Table
1, Panel E). If instead, we add 100,000 workers to a zipcode – about the same as the inter-quartile range
for our sample of office suites – rent would increase by an amount about equal to moving up 27 floors.
These comparisons make clear that nearby employment and vertical location both have economically
important effects on rent.26
Table 3b builds on the model specifications in Table 3a. The key extension here is that zipcode-
level employment is decomposed into employment in and outside of the building. This allows us to
consider whether the intensity of activity inside a building might affect vertical rent gradients. Prior
evidence based on both arrivals of new establishments and wages (e.g., Rosenthal and Strange, 2003,
2008) suggests that agglomeration economies attenuate rapidly with geographic distance. The analogue
here would be that employment inside a building should have a larger effect on rent than employment
outside of the building. Evidence of such a pattern would reinforce the conclusion above that different
mechanisms are driving the vertical and horizontal rent patterns in Table 3a.
To control for building-level employment, we matched tenant records at the street address level to
corresponding street addresses in the Dun and Bradstreet data. D&B data were then used to determine the
level of employment within each of the buildings represented in the CS data file. The matching process
relies on city and street address because the CS data do not provide DUNS numbers for their tenants (the
DUNS number is a unique identifier for each establishment in the D&B database). This and other
features of the matching process make the matching process laborious. For that reason, we have matched
only those CS records found in New York City, the portion of Chicago located in Cook County, and the
portion of San Francisco located in San Francisco County. This leaves us with 28,324 suite observations
spread across 1,192 buildings, roughly 63 percent of which are in New York, 20 percent in Chicago and
17 percent in San Francisco.
Six different models are presented in Table 3b, each of which utilizes a log-linear specification as
we feel that is a more intuitive model to interpret when employment is decomposed into different parts.
Column (1) controls for just zipcode-level employment while column (2) decomposes zipcode

26
It is worth noting that if we omit the MSA fixed effects and estimate the models by OLS, the vertical rent gradient
remains similar to the estimates in Table 3a while the elasticity with respect to zipcode-level employment rises to
roughly 75 percent. This reflects that high employment zipcodes are mostly found in the largest cities (e.g. New
York and Chicago) which tend to have higher rents.

22
employment into employment outside versus inside of the building. Column (3) controls for vertical
location and building height but omits nearby employment. Columns (4) and (5) add the controls for
building height and vertical location to the employment-only models in columns (1) and (2). Column (6)
adds building fixed effects which cause employment and building height to drop out of the model.
Two important patterns jump out from Table 3b. First, the coefficient estimates for the sample in
Table 3b are quite similar to those presented for the larger sample in Table 3a, both with respect to the
influence of zipcode-level employment and vertical location.27 Second, in columns (4) and (5), it is clear
that within building employment and zipcode employment outside of the building both cause rents to
increase but the effect of within-building employment is 3-1/2 times larger. This echoes results from
Rosenthal and Strange (2003, 2004, 2005, 2008, and 2012) and Arzaghi and Henderson (2008) that
agglomeration economies tend to attenuate rapidly with distance. It is noteworthy that this pattern
persists even after controlling for building height, given that building height is positively correlated with
building-level employment.
Summarizing, estimates from this section yield several novel results. First, there is a highly
robust vertical rent gradient. Rents are not at all constant at a given street address. Instead, rents are
characterized by a significant ground floor premium, and an initial sharp decline moving just above the
ground floor. Moving further up within a building, rents rise gradually at low floors and then more
rapidly near the top of the building. These patterns quantitatively important. Second, we obtain a robust
estimate of roughly 10.5 percent for the elasticity of commercial rent with respect to the level of
employment in a building’s zipcode. That estimate is two to five times larger when compared to
analogous estimates that examine the impact of agglomeration on wage rates. Spillover effects are also
much larger when considering the scale of employment inside of a building as compared to nearby
employment just outside, consistent with previous evidence that agglomeration economies attenuate
sharply with distance. What is unique here is that we obtain this evidence using rent as an outcome
measure and based on a spatial organization of activity that specifies an establishment’s building as the
focal point. Third, the vertical and horizontal forces that impact commercial rent are largely independent
from each other. This is consistent with our model, which is based on underlying mechanisms that differ
from those used to explain horizontal variation in productivity and rent.

V. Vertical spatial structure

This section addresses two additional fundamental questions about vertical spatial structure. The
first question is who locates where: in other words, is there systematic sorting by tenant type into different
27
The coefficient on zipcode-level employment in column (1), for example, is 0.0024 compared to the
corresponding estimate of 0.0023 in column (6) of Table 3a. The coefficient on floor number in column (3) is
0.0087 while the corresponding estimate in Table 3a (column (6)) is 0.0074.

23
parts of the building (e.g. ground floor versus above)? The second question is: why? Answering these
questions will provide further evidence of the underlying mechanisms that drive the rent gradients just
documented.

A. Vertical sorting
We begin by considering who locates where. Table 4 describes the vertical distribution of where
tenants are located in the OM data. Distributions are reported for all industries combined (column (1)) as
well as retail (SIC 52-59), not retail, law offices (SIC 81), business services (SIC 73), brokerages offices
(SIC 62), insurance companies (SIC 63), and insurance and brokerage agents (SIC 64). In all cases we
focus only on tenants merged with the D&B data which provides information on the tenant’s SIC code.
For each industry we report the distribution of floor numbers as reflected in the 1st percentile, 25th
percentile, 50th percentile, 75th percentile, and 99th percentile floor number.
The values in Table 4 reveal a striking stratification of industries into different parts of tall
buildings. Retail is almost exclusively concentrated on the ground floor or just above, with a median
location at ground level and the 75th percentile at floor 5. Law offices are especially concentrated higher
up off the ground as are brokerage offices, both of which have median locations just above floor 20 and
75th percentile locations just above floor 30. These patterns reinforce the summary measures in Table 1c
described earlier.

B. Mechanisms: access and amenities

We now move to the second question. Panel B of Table 1 and Table 4 together provide
compelling evidence that retail establishments are heavily concentrated on the ground floor. Section II’s
theory shows that access costs can explain this pattern. Retail establishments rely on frequent interactions
with customers who must travel to the establishment. In this context, total product price to the customer
includes sticker price plus access cost which increases with height off the ground. In the absence of a
positive amenity effect associated with height, retail bid-rents decline with height and retail should sort
into the ground level space as observed. In this sense, we view retail as an access-oriented industry.
Outside of the retail sector the frequency of face-to-face office visits with clients and/or input
providers is much reduced. In addition, the value of the service provided is often much higher both in
comparison to retail and relative to access costs. If this were all that differed between retail and non-
retail, we would have a sufficient condition to ensure that non-retail would sort into locations above the
ground floor, as observed in Table 1 (Panel B) and Table 4. In such an environment, however, office
rents would have to decline in equilibrium with height off the ground to compensate non-retail
establishments for greater travel costs. This, of course, is not consistent with the positive rent gradients

24
documented in Tables 2a, 2b, 3a, and 3b. To allow for those patterns, it must be the case that non-retail
establishments perceive height off the ground as a positive amenity sufficient to offset reduced access.
These arguments confirm a role for both access and amenities and suggest that both increase with height.
Tables 5 and 6 help to clarify how to interpret the positive amenity effect associated with higher
locations in a building. The tables report results from a series of models in which location (measured as
the log of floor number) is regressed on tenant and site characteristics. In all cases, the tables draw
exclusively on D&B data from twelve large metropolitan areas. For reasons to be described shortly, in
most models we restrict our samples to single-site firms in law offices (SIC 81), advertising offices (SIC
7311), brokerage offices (SIC 62), insurance carriers (SIC 63), and agents, brokers and services (SIC 64).
In one model we instead focus exclusively on headquarter establishments for multi-site firms. In that
instance establishments are drawn from all industries.
In both Tables 5 and 6, the two key regressors in the single-site firm models are the sales-per-
worker ratio for the site and the number of employees at the site. Both sales-per-worker and employment
are likely positive correlates with labor productivity. Conditional on employment, a higher ratio of sales-
per-worker suggests that labor is more productive. Productive establishments also tend to grow larger and
operate at a larger scale with more workers on staff. Importantly, higher productivity also likely affects
the intensity of amenity orientation. More productive establishments tend to pay higher wages. Since
amenities such as views are almost certainly normal goods, this will increase the value that the
establishment’s workers place on a location high up in the building, as in Section II. Our motivating
hypothesis is, therefore, that establishments with high sales-per-worker ratios and larger numbers of
workers will have a stronger amenity orientation and greater willingness to pay for locations up high.
This also suggests that companies with high sales-per-worker and larger numbers of employees may favor
higher locations so as to signal to prospective clients and business contacts that they are productive.
Additional controls include 1-0 dummies for whether the establishment belongs to a firm that is
publicly traded or whether the establishment is a subsidiary. Only a small fraction of firms are publicly
traded. Our maintained hypothesis is that these establishments are higher quality in some sense, possibly
rising to the level of “trophy” tenants. For related reasons we also control for subsidiary status although
our prior of how such establishments are perceived is less clear. We also include 1-0 dummies for D&B’s
assessment of risk based on high, medium, and low ratings; coefficients are reported for low and medium
risk with high-risk the omitted category. Lower risk companies may be perceived as more attractive
tenants, ceteris paribus, and for that reason be better fits for high floors. In addition, a tenant’s low-risk
status may also contribute to signaling incentives when choosing where to locate in a tall building.
It is important to note that employing these site-specific characteristics in the estimation requires
that we address the issue of multi-establishment firms. For multi-establishment firms the attribution of

25
sales to sites is uncertain. It is for that reason that we work primarily with single establishment firms.
Multi-establishment firms are interesting, however, so we do consider them in a limited way by
estimating a model of headquarter establishments. We obviously cannot employ the establishment-level
sales-worker ratio in these models. We instead work with the sales-per-worker ratio at the firm level
along with employment at both the firm and establishment levels. The employment variables speak to
productivity, as above.
Consider now column (1) of Table 5 which reports the results for headquarter establishments.
The strongest results are for firm-level sale-per-worker and employment. Larger firms have headquarters
located on higher floors, with an elasticity of 3.5%. Conditional on firm size and the other model
controls, the elasticity associated with sales-per-worker is 2.6 percent. Both of these estimates are also
highly significant (with t-ratios of 5.8 and 5.6, respectively). Other coefficient estimates in the model are
notable but not as dramatic: employment at the site has a small, negative and not significant effect;
publicly traded firms locate 10.6 percent higher (with a t-ratio of 3.18), and lower risk companies are also
higher. Subsidiary status has a negative and marginally significant coefficient of 0.049 (the t-ratio is
1.92), indicating that headquarters of subsidiaries are on somewhat lower floors after controlling for other
factors. Taken as a whole, the estimates in column (1) provide compelling evidence that headquarters of
higher performing companies are located higher up off the ground. It is worth emphasizing that this result
is obtained even after conditioning on the 5-digit zipcode in which a headquarter is located. This pattern
is also echoed in the single-site regressions.
Columns (2) and (3) of Table 5 report results for single-establishment firms pooling data from the
five industries noted above. The model in column (2) controls for both 2-digit industry and 5-digit
zipcode fixed effects while the model in column (3) replaces the zipcode fixed effects with building fixed
effects. The results are similar for the sales-per-worker ratio and for employment at the site. Both are
positively related to floor. The elasticities of floor number with respect to sales-per-worker are 1.4
percent in the zipcode fixed effect model and 1.5 percent in the building fixed effect model with t-ratios
of 2.0 in both cases. For employment at the site the elasticities are 3.0 in the zipcode fixed effect model
and 1.7 in the building fixed effect model (with t-ratios of 6.5 and 5.0, respectively). These results further
reinforce the idea that view amenities raise profit by making it easier to attract productive workers which
should result in lower wages.
Several other patterns in column (2) also suggest that higher performing establishments locate in
higher offices. In particular, the publicly traded dummy is positive and significant in column (2) as are
the coefficients on low and medium risk ratings. These results largely disappear, however, when we shift
from the zipcode fixed effect model in column (2) to the building fixed effect model in column (3). We

26
will comment further on these differences in the context of Table 6 to follow. First, however, we
comment on the industry-stratified models in columns 4-9 of Table 5.
As noted in Table 1, Panel B, law offices account for a significant fraction of office tenants in tall
buildings. Results for law offices are presented in columns (4) and (5) and are qualitatively similar to the
estimates for the pooled samples just described. The primary difference between the two sets of models is
that the magnitude of the sales-per-worker coefficients in the law-office models are larger: 4.6 percent in
the zipcode fixed effect model in column (4) and 2.3 percent in the building fixed effect model in column
(5). These estimates are clearly significant with t-ratios of 4.6 and 2.2, respectively. In the law office
sector, higher productivity companies as proxied by sales-per-worker and number of employees locate
higher up in their immediate zipcode and building.
Estimates for the other industries highlighted above are presented in columns (6) – (9). For these
industries only zipcode fixed effect models are presented given the much smaller sample sizes. Looking
across the columns it is evident that the results are mixed and point to differences in location and sorting
patterns across industries. The results for brokerage offices reported in column (7) are closest to those for
law offices (consistent with patterns in Table 4 and Figure 1). In column (7), notice that the elasticity of
floor number with respect to employment is 4 percent with a t-ratio of 4.6. Agents and Brokers in column
(9) display a similar though more muted result. The other coefficients on sales-per-worker and
employment across the remaining industries are not significant and often rather small in magnitude. On
the other hand, the coefficients on publicly traded companies are revealing. In the case of law offices this
variable is omitted as no law offices are publicly traded. Of the remaining industries, notice that the
coefficient on publicly traded is -0.22 for advertising with a t-ratio of 2.88, and then positive 4.2, 1.3, and
0.6 for the remaining three industries with t-ratios ranging from 2.5 to 45. We do not have a good
explanation for why publicly traded advertising establishments are located on lower floors. Nevertheless,
for the other industries the large positive, significant elasticities are consistent with the view that publicly
traded companies are higher end (higher productivity) and locate higher up in tall buildings for reasons
described earlier.
Table 6 revisits the models for the pooled industries and law offices. In each case models are
presented for OLS specifications, MSA fixed effects, zipcode fixed effects, and building fixed effects.
This allows us to highlight systematic differences in patterns as the geographic nature of the controls
becomes more refined. The coefficients on sales-per-worker and employment at the site diminish in
magnitude as the geographic scope of the fixed effects narrow to that of individual buildings. A similar
pattern is present for the other model controls (e.g. publicly traded, risk). It is worth recalling that the
fixed effects capture the influence of unobserved factors common to the observations associated with the
fixed effect. Accordingly, the patterns in Table 6 suggest that establishments tend to sort across locations

27
down to the building level in a manner that is correlated with sales-per-worker and the other model
controls. This indicates that high productivity companies concentrate in select zipcodes and buildings,
although the models in Table 6 do not highlight which attributes of a zipcode or building tend to attract
productive companies.

VI. Conclusion

Two ongoing trends are changing the shape and nature of cities. The first is that the number of
skyscrapers is growing rapidly, as is the level of employment housed in tall buildings. The second is that
business services are located disproportionately in tall buildings and account for an increasing share of
employment in city centers. Nevertheless, standard urban models have emphasized horizontal patterns of
development, while research on agglomeration economies has tended to focus on manufacturing, which is
most often found in low-rise buildings.
This paper departs from conventional urban economic analysis by modeling vertical patterns in
the tall commercial buildings that dominate city skylines. The paper’s theory predicts systematic vertical
sorting based on the tension between vertical access costs and amenities, both of which increase with
height off of the ground. Consistent with the theory, empirical analysis confirms that high productivity
amenity-oriented office companies locate high up, with less productive offices lower down. Retail
tenants, who are strongly access-oriented, concentrate at ground level. These sorting patterns support a
non-monotonic, nonlinear vertical rent gradient, with rents falling initially as one moves up off the ground
floor, but then rising above the second floor at a modest rate that increases with height.
The magnitude of vertical variation in rent rivals that of horizontal variation associated with the
scale of nearby employment. Doubling employment in a building’s zipcode increases commercial rent by
roughly 10.5 percent, on average. The impact of within-building employment is even larger, a result that
reinforces previous evidence from wage and other related studies that productivity spillovers from
agglomeration attenuate rapidly with distance (e.g. Rosenthal and Strange (2001, 2003, 2005, 2008),
Arzaghi and Henderson (2008), and Baum-Snow (2011)). In comparison, adding 100,000 workers to a
building’s zipcode has roughly the same impact on commercial rent as moving up 30 floors.
Finally, we find that the vertical rent gradient is independent of the scale of nearby employment.
This includes the level of employment in the building itself as well as nearby employment outside of the
building. The agglomeration literature has pointed to opportunities to share skilled labor, intermediate
inputs and knowledge as key determinants of productivity spillovers from nearby activity. Our finding
that vertical rent gradients are independent of the scale of nearby employment confirms that vertical rent
patterns are driven by a different set of mechanisms, consistent with our model.

28
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 Table 1: Summary Measures

Panel A: Three Data Sources

Dun and Bradstreet
Dun and Bradstreet For 5 Industries
Offering Memo CompStak Merged with Not Merged with
(OM) (CS) OM Data OM or CS Dataa
Number of Buildings 93 1,922 93 19,721
Number of Tenant-Suite Obs 5,750 37,007 5,472 57,748
Number of MSAs 18 8 18 12
Time Period for Data 2003 - 2014 1999 - 2015 2014 2015

Panel B: Industry Composition in Offering Memo Tall Buildings in Percentb

Ground Floor and Floor > 2
All Floors Concourse and < 40 Floor >= 40
Retail (SIC 52-59) 6.79 32.71 2.34 3.45
FIRE (SIC 60-67) 23.43 10.12 25.74 25.43
Business Services (SIC 73) 8.43 7.76 8.62 8.19
Law Offices (SIC 81) 20.31 8.24 20.65 43.10
Eng, Acc, Man (SIC 87) 12.13 2.59 14.00 11.64
All Other Industries 28.91 38.58 28.65 8.19

Panel C: Commercial Rents Per Square Foot ($2014)

Average 25th percentile 50th percentile 75th percentile
Offering Memo Data 38 22 33 51
CompStak Data 36 17 33 49

Panel D: Building Height in Number of Floors

Average Median % Over % Over Minimum Maximum

Floor Floor Floor 30 Floor 60 Floor Floor
By Building
Offering Memo (93) 32.7 28 47.3% 4.3% 16 109
CompStak (1,922) 21.5 17 21.2% 1.3% 10 109
By Tenant Suite
Offering Memo Data (5,750) 39.5 34 59.9% 10.5% 16 109
CompStak Data (37,007) 30.5 27 46.9% 3.9% 10 109

Panel E: Zipcode Employment in Which CompStak Buildings are Located (in 1,000 units)
Average 1st Pctl 25th Pctl 50th Pctl 75th Pctl 99 Pctl
By Zipcode (193 zipcodes) 36.21 0.96 18.66 28.72 44.83 142.45
By Tenant Suite (36,963 suites) 85.11 11.72 42.72 78.38 134.99 146.22
a
The metropolitan areas include New York, Chicago, San Francisco, Los Angeles, Atlanta, Washington DC, Cleveland,
Detroit, Dallas, Denver, Houston, and Seattle. The industries include law offices (SIC 81), advertising offices (SIC
7311), brokerage offices (SIC 62), insurance carriers (SIC 63), and agents, brokers and services (SIC 64).
b
Based on the OM data merged with D&B.

33
 Table 2a: Rent Gradients with Building Fixed Effectsa
(t-ratios based on standard errors clustered at the building level)
Offering Memo Data CompStak Data
Below ground floor -0.0425 -0.3398 - -
(-0.25) (-2.73) - -
Ground floor 0.5148 0.3160 0.1156 0.0295
(4.99) (2.16) (3.16) (0.81)
Ground Floor X Bldg Height 0.0070 0.0113 0.0070 0.0073
(1.89) (1.91) (3.96) (4.15)
Log(Floor number + k)b 0.2854 - 0.0858 -
(2.52) - (16.89) -
Floor number - 0.0173 - 0.0058
- (2.73) - (17.31)
Observations 5,510 5,510 37,007 37,007
Lease quarter Fixed Effects - - Yes Yes
Building Fixed Effects 93 93 1,922 1,922
R-sq within 0.065 0.106 0.247 0.254
a
Dependent variable for the OM regressions is gross rent per square foot in $2014. Dependent variable
for the CS regressions is in $2014 and is net rent which adjusts gross rent for months of free rent at the
start of the lease and other accommodations.
b
k is set to a value 1 unit larger in absolute value than the lowest basement floor in the data, -5 for the
offering memo data and -1 for the CompStak data.

34
 Table 2b: Convex Rent Gradientsa
(t-ratios based on standard errors clustered at the building level)
Offering Memo Data CompStak Data
(1) (2) (3) (4) (5) (6)
Floors 3 Floors 30 Floors 60 Floors 3 Floors 30 Floors 60
through 29 through 59 and above through 29 through 59 and above
PANEL A: Double Log
Log(Floor number + k)b 0.1447 0.1352 5.40 0.0760 0.2873 1.274
(4.31) (0.81) (649.37) (16.55) (7.29) (4.20)
Observations 3,537 775 146 29,360 4,602 116
Lease quarter Fixed Effects No No No Yes Yes Yes
Building Fixed Effects 93 44 4 1,862 369 18
R-sq within 0.019 0.003 0.090 0.257 0.295 0.710

PANEL B: Log-Linear
Floor number 0.0082 0.0033 0.0620 0.0058 0.0068 0.0161
(4.30) (0.89) (362.06) (17.41) (7.30) (4.95)
Observations 3,537 775 146 29,360 4,602 116
Lease quarter Fixed Effects No No No Yes Yes Yes
Building Fixed Effects 93 44 4 1,862 369 18
R-sq within 0.019 0.003 0.090 0.259 0.295 0.708
a
Dependent variable for the OM regressions is gross rent per square foot in $2014. Dependent variable for the CS
regressions is in $2014 and is net rent which adjusts gross rent for months of free rent at the start of the lease and other
accommodations.
b
k is set to a value 1 unit larger in absolute value than the lowest basement floor in the data, -5 for the offering memo
data and -1 for the CompStak data.

35
 Table 3a: Vertical Versus Horizontal Rent Gradients Using CompStak Dataa
(t-ratios based on standard errors clustered at the building level)

Double-Log Models Log-Linear Models

(1) (2) (3) (4) (5) (6) (7) (8)
MSA FE MSA FE MSA FE Bldg FE MSA FE MSA FE MSA FE Bldg FE
Building height (floors) - 0.0024 0.0021 - - 0.0018 0.0011 -
- (2.68) (2.25) - - (2.00) (1.30) -
Ground floor - 0.1787 0.1813 0.1156 - 0.0537 0.0556 0.0295
- (4.55) (4.48) (3.16) - (1.36) (1.37) (0.81)
Ground Floor X Bldg Height - 0.0072 0.0072 0.0070 - 0.0075 0.0076 0.0073
- (3.86) (3.70) (3.96) - (4.09) (3.99) (4.15)
Log(Floor number + k)b - 0.1165 0.1157 0.0858 - - - -
- (12.98) (13.14) (16.89) - - - -
Floor number - - - - - 0.0074 0.0073 0.0058
- - - - - (12.90) (13.75) (17.31)
Log(Zipcode emp in 1,000) 0.1068 - 0.0931 - - - - -
(5.42) - (4.93) - - - - -
Zipcode emp (1,000s) - - - - 0.0023 - 0.0020 -
- - - - (7.62) - (6.96) -
Observations 36,963 37,007 36,963 37,007 36,963 37,007 36,963 37,007
Lease quarter Fixed Effects Yes Yes Yes Yes Yes Yes Yes Yes
MSA Fixed Effects 8 8 8 No 8 8 8 No
Building Fixed Effects No No No 1,922 No No No 1,922
R-sq within - - - 0.247 - - - 0.254
R-sq total 0.881 0.887 0.889 0.945 0.884 0.887 0.891 0.945
a
Dependent variable is in $2014 and is net rent which adjusts gross rent for months of free rent at the start of the lease and other accommodations.
b
k is set to a value 1 unit larger in absolute value than the lowest basement floor in the data, -5 for the offering memo data and -1 for the CompStak data.

36
 Table 3b: New York City, Chicago, and San Francisco Rent Gradients Controlling for Building-Level Employmenta
(t-ratios based on standard errors clustered at the building level)
(1) (2) (3) (4) (5) (6)
Building height (floors) - - 0.0021 0.0115 0.0009 -
- - (2.00) (1.44) (0.89) -
Ground floor - - 0.1875 0.1996 0.1969 0.1407
- - (2.61) (2.76) (2.71) (2.14)
Ground Floor X Bldg Height - - 0.0056 0.0052 0.0051 0.0055
- - (2.09) (1.96) (1.92) (2.26)
Floor number - - 0.0087 0.0085 0.0084 0.0064
- - (14.45) (15.28) (15.44) (18.42)
Zipcode emp (1,000s) 0.0024 - - 0.0022 - -
(7.63) - - (6.94) - -
Zipcode – Bldg emp (1,000s) - 0.0023 - - 0.0021 -
- (7.19) - - (6.76) -
Building employment (1,000s) - 0.0113 - - 0.0073 -
- (3.87) - - (2.75) -
Chicago -0.904 -0.9004 -0.1.026 -0.9460 -0.9395 -
(-28.93) (-28.92) (-33.50) (-28.17) (-27.96) -
San Francisco -0.0546 -0.0489 -0.1442 -0.0354 -0.0344
(-1.99) (-1.81) (-7.01) (-1.40) (-1.36)
Observations 28,324 28,324 28,324 28,324 28,324 28,324
Lease quarter Fixed Effects Yes Yes Yes Yes Yes Yes
Building Fixed Effects No No No No No 1,192
R-sq within - - - - - 0.294
R-sq total 0.565 0.573 0.584 0.604 0.607 0.798
a
Dependent variable is log of net rent which adjusts gross rent for months of free rent at the start of the lease and other
accommodations.

37
 Table 4: Vertical Location By Industrya

(1) (2) (3) (4) (5) (6) (7) (8)

Insurance
Brokerage Insurance Agents,
Not Retail Business Offices Carriers Brokers &
All Retail (Not Sic2 Services Law Offices 12 MSAs 12 MSAs Services
Industries (Sic2 52-59) 52-59) (Sic2 73) (Sic2 81) (SIC 62) (SIC 63) (SIC 64)
st
1 Pctl -2 -2 -2 -2 -1 -2 -1 -1
25th Pctl 4 1 7 5 14 12 7 9
50th Pctl 14 1 16 15 21 23 13 18
75th Pctl 25 5 26 25 33 31 26 26
th
99 Pctl 97 90 66 93 72 55 61 43
# Obs 5,750 226 2,940 267 643 277 63 76
a
Offering memo data for 93 buildings for tenants matched to D&B records.

38
 Table 5: Location by Sales per Worker
(Dependent Variable: Log Floor Number)a

(1) (2) (3) (4) (5) (6) (7) (8) (9)

Insurance
Agents,
Advertising Brokerage Insurance Brokers &
Head Law Offices Law Offices Offices Offices Carriers Services
Quarters Single Site Single Site 12 MSAs 12 MSAs 12 MSAs 12 MSAs 12 MSAs 12 MSAs
12 MSAs 12 MSAsb 12 MSAsb (SIC 81) (SIC 81) (SIC 7311) (SIC 62) (SIC 63) (SIC 64)
Log sales/worker at site - 0.0139 0.0149 0.0463 0.0225 -0.0353 0.0040 -0.0227 -0.0064
- (2.01) (2.00) (4.61) (2.21) (-1.28) (0.26) (-1.24) (-0.43)
Log employment at site -0.0110 0.0304 0.0169 0.0372 0.0134 0.0065 0.0406 -0.0112 0.0160
(-1.40) (6.47) (5.03) (6.03) (3.37) (0.47) (4.56) (-0.58) (2.35)
Log sales/worker – Firm 0.0262 - - - - - - - -
(5.64) - - - - - - - -
Log employment – Firm 0.0352 - - - - - - - -
(5.84) - - - - - - - -
Publicly traded 0.1061 0.5371 0.2265 - - -0.2242 0.4196 1.3266 0.6150
(3.18) (1.84) (0.89) - - (-2.88) (2.49) (7.13) (45.89)
Subsidiary -0.0488 0.0029 -0.0819 0.0523 -0.0244 0.0741 -0.0184 0.0599 0.0501
(-1.92) (0.11) (-2.38) (0.38) (-0.18) (0.85) (-0.45) (0.66) (1.06)
Risk Rating: Low 0.0286 0.0284 0.0003 0.0331 -0.0046 0.0364 0.0450 -0.0216 0.0058
(1.69) (2.73) (0.04) (2.47) (-0.45) (0.67) (1.30) (-0.23) (0.35)
Risk Rating: Medium 0.0680 0.0432 -0.0225 0.0372 -0.0315 0.0547 0.0300 0.0982 0.0456
(2.37) (2.41) (-1.76) (1.26) (-1.96) (0.83) (0.86) (0.86) (1.78)
Observations 16,335 58,389 58,389 36,980 36,980 1,700 6,884 1,268 10,916
Within R-squared 0.013 0.010 - 0.004 - 0.003 0.005 0.014 0.002
Total R-squared - - 0.8141 - 0.8207 - - - -
2-digit Industry FE - 5 5 - - - - - -
5-Digit Zipcode FE 640 1,767 - 1,493 - 428 1,001 574 1,460
Building FE - - 19,721 - 11,955 - - - -
a
Data are from Dun and Bradstreet. T-ratios in parentheses based on standard errors clustered at the level of the geographic fixed effects (zipcode or building).
b Includes SIC 62, 63, 64, 7311, 81.

39
 Table 6: Alternate Geographic Fixed Effects
(Dependent Variable: Log Floor Number)a

(1) (2) (3) (4) (5) (6) (7) (8)

Pooled Data for Five 2-Digit
Single Site Industries in 12 MSAsb Law Offices in 12 MSAs (SIC 81)
MSA 5-Digit Zip Building MSA 5-Digit Zip Building
Fixed Fixed Fixed Fixed Fixed Fixed
OLS Effects Effects Effects OLS Effects Effects Effects
Log sales/worker at site 0.0977 0.0635 0.0139 0.0149 0.1635 0.1238 0.0463 0.0225
(12.11) (7.42) (2.01) (2.00) (11.35) (10.02) (4.61) (2.21)
Log employment at site 0.0860 0.0842 0.0304 0.0169 0.0873 0.0909 0.0372 0.0134
(22.88) (9.22) (6.47) (5.03) (17.34) (7.36) (6.03) (3.37)
Publicly traded 0.7563 0.6450 0.5371 0.2265 - - - -
(2.90) (19.53) (1.84) (0.89) - - - -
Subsidiary 0.2242 0.1673 0.0029 -0.0819 0.1712 0.0631 0.0523 -0.0244
(6.84) (2.96) (0.11) (-2.38) (1.29) (0.50) (0.38) (-0.18)
Risk Rating: Low 0.0566 0.0679 0.0284 0.0003 0.0835 0.0902 0.0331 -0.0046
(5.47) (5.93) (2.73) (0.04) (6.21) (5.48) (2.47) (-0.45)
Risk Rating: Medium 0.1455 0.1076 0.0432 -0.0225 0.1595 0.1178 0.0372 -0.0315
(10.19) (4.37) (2.41) (-1.76) (7.95) (3.14) (1.26) (-1.96)
Observations 58,389 58,389 58,389 58,389 36,980 36,980 36,980 36,980
Within R-squared 0.081 0.071 0.010 - 0.014 0.013 0.004 -
Total R-squared - - - 0.814 - - - 0.821
2-digit Industry FE 5 5 5 5 - - - -
MSA FE - 12 - - - 12 - -
5-Digit Zipcode FE 215 - 1,749 - - - 1,493 -
Building FE - - - 19,721 - - - 11,955
a Data are from Dun and Bradstreet. T-ratios in parentheses based on standard errors clustered at the level of the fixed effects.
b Includes SIC 62, 63, 64, 7311, 81.

40
 Appendix A: Offering Memo Example
JP Morgan Chase Commercial Mortgage Securities Trust 2006-LDP728

One Prudential Plaza Stacking Plan

Flr Tenant SqFt Lease Tenant SqFt Lease

Ends Ends
41 Plaza Club 7,798 06/06
40M AM/FM Ohio, Inc 100 09/06
40 Vacant 1,860 Multi-Tenant 8,254
39 Baker & McKenzie LLP 22,503 11/12
38 Schuyler, Roche & Zwirner 24,082 04/15
37 Baker & McKenzie LLP 24,017 11/12
36 Baker & McKenzie LLP 24,068 11/12
35 Baker & McKenzie LLP 24,148 11/12
34 Vacant 14,274 Baker & McKenzie LLP 8,917 12/08
33 Baker & McKenzie LLP 23,026 11/12
32 Baker & McKenzie LLP 22,411 11/12
31 Baker & McKenzie LLP 22,990 11/12
30 Baker & McKenzie LLP 21,191 11/12
29 McGraw-Hill Inc 22,647 11/16
28 Baker & McKenzie LLP 9,747 11/12 BDO Seidman, LLP 12186 09/11
27 Bonneville International 21,913 05/18
26 Multi-Tenant 21,742
25 Baker & McKenzie LLP 22,862 11/12
24 Peoples Gas Light & Coke 21,803 05/14
23 Peoples Gas Light & Coke 21,803 05/14
22 Peoples Gas Light & Coke 21,803 05/14
21 Peoples Gas Light & Coke 22,862 05/14
20 Peoples Gas Light & Coke 23,264 05/14
19 Peoples Gas Light & Coke 21,321 05/14
18 Peoples Gas Light & Coke 19,917 05/14
17 Peoples Gas Light & Coke 23,203 05/14
16 Peoples Gas Light & Coke 23,126 05/14
Atty Regis & Disciplinary
15 Commission 23,125 05/15
14 Vacant 1,208 McGraw-Hill, Inc 23,199 11/16
13 Vacant 22,398 BDO Seidman, LLP 383 09/06
12 Vacant 1,991 Multi-Tenant 21,375
11 Multi-Tenant 22,397
10 Vacant 1,009 Multi-Tenant 47,600
9 McGraw-Hill, Inc 49,998 11/16
8 Vacant 48,818
7 Vacant 19,655 Kirkland & Ellis LLP 28,154 12/11
6 Kirkland & Ellis LLP 52,224 21/11
5 BCE Nexxia Corp 49,144 08/15
4 McGraw-Hill, Inc 49,252 11/16
3 Peoples Gas Light & Coke 48,784 05/14

28
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41
 Appendix A (continued)
JP Morgan Chase Commercial Mortgage Securities Trust 2006-LDP729

One Prudential Plaza Stacking Plan

Flr Tenant SqFt Lease Tenant SqFt Lease

Ends Ends
2 Vacant 5 Multi-Tenant 36,763
1 Vacant 19,239 Multi-Tenant 22,151
Entr Vacant 2,011 Multi-Tenant 34,148
B2 Peoples Gas Light & Coke 267 05/14
B1 Vacant 8,005 Multi-Tenant 9,662

Two Prudential Plaza Stacking Plan

Flr Tenant SqFt Lease Tenant SqFt Lease

Ends Ends
58 Taipei Econ/ Cultural Ofc 12,994 06/11
57 Taipei Econ/ Cultural Ofc 10,267 06/11 Advisory Research Inc. 2,943 05/14
58 Taipei Econ/ Cultural Ofc 12,994 06/11
56 Prudential Insurance Co. 13,717 07/08
55 Multi-Tenant 14,000
54 Prudential Insurance Co. 14,082 07/08
53 Multi-Tenant 12,822 Vacant 1,325
52 Vacant 14,038
51 Centraxcorp 14,932 03/16
50 Leydig, Voit & Mayer Ltd 15,164 08/10
49 Leydig, Voit & Mayer Ltd 16,000 08/10
48 Leydig, Voit & Mayer Ltd 16,000 08/10
47 Leydig, Voit & Mayer Ltd 9,704 08/10 Prudential Insurance Co. 7,540 07/08
46 Prophet Brand Strategy 17,950 03/12
45 Multi-Tenant 17,950
44 International Food Svc 9,747 11/13 Vacant 8,203
43 Black Entertainment TV 9,647 08/07 BDO Seidman, LLP 8,303
42 Aleri, Inc 18,726 10/07
41 Aleri, Inc 19,000 10/07
40 Aleri, Inc 19,565 10/07
39 Mechanical Room
38 Bowman, Barrett & Assoc 162 11/06 Mechanical Room 1,313 38
37 Leboeuf, Lamb, Greene & 20,184 09/10
Macrae
36 Norgren, Inc 6,560 09/12 Vacant 13,555
35 Vacant 20,174
34 Vacant 20,743
33 Vacant 20,219
32 Multi-Tenant 18,223 Vacant 2,007
Appendix B (continued)
JP Morgan Chase Commercial Mortgage Securities Trust 2006-LDP730

29
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42
 Two Prudential Plaza Stacking Plan (continued)

Flr Tenant SqFt Lease Tenant SqFt Lease

Ends Ends
31 Multi-Tenant 19,865
30 Multi-Tenant 19,893
29 Aon Corporation 20,966 09/09
28 Aon Corporation 20,966 09/09
27 Aon Corporation 20,992 09/09
26 Multi-Tenant 20,447
25 Multi-Tenant 20,059
24 Multi-Tenant 18,174 Vacant 1,731
23 Vacant 19,922
22 Vacant 19,936
21 Michael Best&Friedric LLP 20,157 01/17
20 Michael Best&Friedric LLP 20,655 01/17
19 Michael Best&Friedric LLP 3,599 01/17 Vacant 17,052
18 Amsted Industries, Inc 17,040 11/18 Singapore Econ Dev 3,578 03/09
17 SAS Institute, Inc. 20,611 12/15
16 SAS Institute, Inc. 8,504 12/15 Vacant 12,089
15 Vacant 20,571
14 Vacant 20,571
13 Multi-Tenant 10,256 Vacant 9,702
12 Vacant 20,762
11 Infinity Holdings Corp. 21,548 04/18 Vacant 316
10 Infinity Holdings Corp. 20,580 04/18
9 Infinity Holdings Corp. 21,145 04/18
8 Multi-Tenant 15,718 Vacant 5,344
7 Doubleclick, Inc. 9,801 07/10 Vacant 11,590
6 Kirkland & Ellis LLP 21,420 12/11
5 Multi-Tenant 4,034
4 Multi-Tenant 5,885 Vacant 1,375
2 Las Vegas Convention 2,380 08/15 Mechanical Room
Visitors Authority
1 Multi-Tenant 9,230 Vacant 1,841
Entr Schermerhorm 300 10/09 Vacant 1,608
B1 Multi-Tenant 900 Vacant 600

43
 Appendix B: Rent Roll Example
A Portion of the Rent Roll for 999 Peachtree (2/28/2013)31

31
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44
 Appendix B (continued): Rent Roll Example
A Portion of the Rent Roll for 999 Peachtree (2/28/2013)

45